All magnetic materials have hysteresis. Hysteresis, specifically, magnetic hysteresis, refers to the history dependent nature of the magnetic field applied to the material. Because a magnetoresistive (MR) sensor such as a giant magnetoresistive (GMR) sensor is made of magnetic material, its response exhibits the effects of hysteresis. A plot of resistance against applied magnetic field forms a hysteresis loop, as the change in resistance in the forward direction (for increasing applied magnetic field) and the reverse direction (for decreasing applied magnetic field) are not the same. The hysteresis loop thus shows that the resistance doesn't just depend on the applied magnetic field, but also on what the applied magnetic field was previously.
The error resulting from the hysteresis takes the form of a direct current (DC) offset in the sensor output. Although MR sensors such as GMR sensors generally offer higher sensitivity than other types of magnetic field sensors, for example, Hall Effect sensors, they are not presently used for high resolution sensor applications because of their hysteresis characteristics.